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Stability of nonautonomous difference equations with several delays

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Abstract

We consider the possibility to construct efficient stability criteria for solutions to difference equations with variable coefficients. We prove that one can associate a difference equation with a certain functional differential equation, whose solution has the same asymptotic behavior. We adduce examples, demonstrating the essential character of conditions of the obtained theorems and the exactness of the constant 3/2 which defines the boundary of the stability domain.

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Correspondence to A. Yu. Kulikov.

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Original Russian Text © A.Yu. Kulikov, V.V. Malygina, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 3, pp. 18–26.

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Kulikov, A.Y., Malygina, V.V. Stability of nonautonomous difference equations with several delays. Russ Math. 52, 15–23 (2008). https://doi.org/10.3103/S1066369X0803002X

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  • DOI: https://doi.org/10.3103/S1066369X0803002X

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